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Unformatted text preview: Econ 310-2 Solutions to Problem Set #1 1 TA: Oscar F Contreras 1 Exercise 1 Remember that by assumption all social preferences are transitives. Further, note that all of the examples of social preferences are also complete. Therefore, given the information provided in the question, UD is never violated. (a) IIA is violated. Notice that from line 1 to 2 the ranking of B relative to A didnt change for either consumer (Jesse prefers A to B in both cases and Erika prefers B to A in both cases). Yet, the social ranking did change (first A is preferred to B and then B is preferred to A). Hence, the IIA condition is violated (here, C is an irrelevant alternative for deciding between A and B that ends up changing the social ranking). (b) PC is violated. Both consumers agree A is better than B but the social preference ranks B * A . (c) Sarah is a dictator. The social ranking coincides with Sarahs ranking for every preference profile. (d) IIA is violated. Notice that from line 1 to 2 both consumers maintain the same relative ranking between A and C (Howard thinks A is better than C and Michael thinks C is better than A). However, the social ranking between A and C changed (in line 1 A is better than C while the opposite is true in line 2). Thus, IIA is violated (here, B is the irrelevant alternative for deciding between A and C that ends up changing the social ranking). Notice that you can make the same argument with alternatives A and D. 2 Exercise 2 (a) UD could or could not be satisfied. If the constant social ranking is complete and transitive, then UD is satisfied. Otherwise UD will be violated. PC is violated. Consider any (finite) number of alternatives ( l > 1), any (fi- nite) number of individuals ( n > 1), and any ranking over the set of alternatives 1 I thank Tuan Hwee Sng and Pablo Schenone. Of course, all errors are mine. Please email me if you find any errors/typos. Thanks :) 1 (this ranking will represent the constant social preference). Choose two alter-(this ranking will represent the constant social preference)....
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- Spring '08